Econometric Analysis of Panel Data Panel Data Analysis – Random Effects Assumptions GLS Estimator Panel-Robust Variance-Covariance Matrix ML Estimator – Hypothesis Testing Test for Random Effects Fixed Effects vs. Random Effects

Panel Data Analysis Random Effects Model – u i is random, independent of e it and x it. – Define it = u i + e it the error components.

Random Effects Model Assumptions – Strict Exogeneity X includes a constant term, otherwise E(u i |X)=u. – Homoschedasticity – Constant Auto-covariance (within panels)

Random Effects Model Assumptions – Cross Section Independence

Random Effects Model Extensions – Weak Exogeneity – Heteroscedasticity and Autocorrelation – Cross Section Correlation

Model Estimation: GLS Model Representation

Model Estimation: GLS GLS

Model Estimation: RE-OLS Partial Group Mean Deviations

Model Estimation: RE-OLS Model Assumptions OLS

Model Estimation: RE-OLS Need a consistent estimator of : – Estimate the fixed effects model to obtain – Estimate the pooled model to obtain – Based on the estimated large sample variances, it is safe to obtain

Model Estimation: RE-OLS Panel-Robust Variance-Covariance Matrix – Consistent statistical inference for general heteroscedasticity, time series and cross section correlation.

Model Estimation: ML Log-Likelihood Function

Model Estimation: ML ML Estimator

Hypothesis Testing Test for Var(u i ) = 0, that is – If T i =T for all i, the Lagrange-multiplier test statistic (Breusch-Pagan, 1980) is:

Hypothesis Testing – For unbalanced panels, the modified Breusch- Pagan LM test for random effects (Baltagi-Li, 1990) is: – Alternative one-side test:

Hypothesis Testing Fixed Effects vs. Random Effects EstimatorRandom Effects E(u i |X i ) = 0 Fixed Effects E(u i |X i ) =/= 0 GLS or RE-OLS (Random Effects) Consistent and Efficient Inconsistent LSDV or FE-OLS (Fixed Effects) Consistent Inefficient Consistent Possibly Efficient

Hypothesis Testing Fixed effects estimator is consistent under H 0 and H 1 ; Random effects estimator is efficient under H 0, but it is inconsistent under H 1. Hausman Test Statistic

Hypothesis Testing Alternative Hausman Test – Estimate the random effects model – F Test that = 0

Example: Investment Demand Grunfeld and Griliches [1960] – i = 10 firms: GM, CH, GE, WE, US, AF, DM, GY, UN, IBM; t = 20 years: – I it = Gross investment – F it = Market value – C it = Value of the stock of plant and equipment